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Adaptive robust control of nonholonomic systems with stochastic disturbances. (English) Zbl 1117.93027
Summary: This paper deals with nonholonomic systems in chained form with unknown covariance stochastic disturbances. The objective is to design the almost global adaptive asymptotical controllers in probability ${u}_{0}$ and ${u}_{1}$ for the systems by using discontinuous control. A switching control law ${u}_{0}$ is designed to almost globally asymptotically stabilize the state ${x}_{0}$ in both the singular ${x}_{0}\left({t}_{0}\right)=0$ case and the non-singular ${x}_{0}\left({t}_{0}\right)\ne 0$ case. Then the state scaling technique is introduced for the discontinuous feedback into the $\left({x}_{1},{x}_{2},\cdots ,{x}_{n}\right)$-subsystem. Thereby, by using backstepping technique the global adaptive asymptotical control law ${u}_{1}$ has been presented for $\left({x}_{1},{x}_{2},\cdots ,{x}_{n}\right)$-subsystem for both different ${u}_{0}$ in non-singular ${x}_{0}\left({t}_{0}\right)\ne 0$ case and the singular case ${x}_{0}\left({t}_{0}\right)=0$. The control algorithm validity is proved by simulation.
MSC:
 93B35 Sensitivity (robustness) of control systems 93C42 Fuzzy control systems 93E03 General theory of stochastic systems 93E15 Stochastic stability
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